WASHINGTON — President Barack Obama seized on the re-emergence of an ambitious bipartisan budget plan in the Senate on Tuesday to invigorate his push for a big debt-reduction deal, and he summoned congressional leaders back to the bargaining table this week to “start talking turkey.”

The bipartisan proposal from the so-called Gang of Six senators to reduce deficits by nearly $4 trillion over the coming decade — and its warm reception from 43 other senators of both parties — renewed hopes for a deal, days after talks between Obama and congressional leaders had reached an impasse.

Financial markets rallied on the news. And with time running out before the deadline of Aug. 2 to raise the government’s $14.3 trillion debt ceiling, Obama’s quick embrace of the plan left House Republicans at greater risk of being politically isolated on the issue if they continue to rule out any compromise that includes higher tax revenue.

Rep. Eric Cantor, the House majority leader who has led opposition to any deal including tax increases, later issued a statement saying the bipartisan Senate plan includes “some constructive ideas to deal with our debt.”

But he stopped far short of endorsing it. House Republicans passed legislation Tuesday evening calling for deep spending cuts and the adoption of a constitutional amendment requiring a balanced budget. Though the legislation has no chance of passing the Senate, the 234-to-190 vote was a symbolic statement by conservatives heading into the end game of a confrontation whose economic and political stakes are hard to overstate.

The Senate group’s plan, modeled on the recommendations last year of a bipartisan fiscal commission established by Obama, calls for both deep spending cuts and new revenue through an overhaul of the income-tax code.

But while its sponsorship by staunch conservatives as well as liberals suggested enough flexibility within both parties to get a deal eventually, it would be all but impossible to turn it into detailed legislation — at the moment it is a four-page outline — and pass it in less than two weeks. Both parties were considering ways to use the proposal as the basis for a broader budget agreement if they can find a way to get past the immediate pressure to increase the debt limit.

Sen. Coburn returns

Tuesday marked the return to the bipartisan Senate group of Sen. Tom Coburn, a conservative Republican of Oklahoma, two months after he abandoned the effort by two other Republicans and three Democrats to reach a deal, saying it would not cut spending enough. Monday, he had laid out his own $9 trillion debt-reduction plan, but acknowledged it could not pass.

Coburn’s willingness to sign on to the bipartisan approach signaled that at least some conservatives, having made their point, might be ready to bargain.

And Republicans increasingly are showing signs of splintering. Some conservatives within Congress and outside have become increasingly vocal in asserting that the party is at risk of putting ideological purity ahead of the chance for a major deficit reduction that includes substantial Democratic concessions, including cuts in Social Security, Medicare and Medicaid spending.

In appearing in the White House briefing room just hours after the Gang of Six went public with its proposal, Obama sought to use the development to increase the pressure on House Republicans even as they moved toward a vote on their bill.

The bill passed by the House would slash spending for next year, cap future spending levels and advance a constitutional amendment requiring a balanced budget. Its passage was a rejoinder of sorts to a plan hatched by the Republican leader, Sen. Mitch McConnell of Kentucky, that would allow Republicans to accede to a $2.4 trillion increase in the government’s debt limit without actually voting for it, but also without the dollar-for-dollar spending cuts that House Republicans had demanded in return.

2012 election issue

Democrats are certain to make the House Republicans’ proposal an issue in the 2012 elections, along with the House Republicans’ budget passed earlier this year that would remake Medicare and Medicaid. But most attention shifted to the Gang of Six blueprint, and the reaction to it from the White House and congressional leaders, who were cooler to it than Obama.

While Obama said he did not agree with all of the senators’ plan, by his endorsement of its thrust and his remarks to reporters, he plainly sought to isolate further the House Republicans.

“We have a Democratic president and administration that is prepared to sign a tough package that includes both spending cuts and modifications to Social Security, Medicaid and Medicare that would strengthen those systems” while also providing new revenues, Obama said. And, he added, “we now have a bipartisan group of senators” and a majority of Americans who agree with such a balanced approach.

Forty-nine senators, 25 Democrats and 24 Republicans, were present for a closed-door meeting in the Capitol where those in the Gang of Six, except Coburn, outlined the debt-reduction plan that had been seven months in the works.

“It is early to say, but their timing is good,” said Sen. Lamar Alexander, R-Tenn. He added, “It helps that the three Republicans senators are three of the most conservative, most respected members of the Senate who are Republicans.”

Besides Coburn, those are Sens. Michael Crapo of Idaho and Saxby Chambliss of Georgia, who formed the group with Sen. Mark Warner, D-Va. The other two Democrats are Sens. Richard Durbin of Illinois and Kent Conrad of North Dakota, chairman of the Senate Budget Committee.